Regularity of stochastic kinetic equations

Hypoelliptic Regularity in Kinetic Equations

We establish new regularity estimates, in terms of Sobolev spaces, of the solution f to a kinetic equation. The right-hand side can contain partial derivatives in time, space and velocity, as in classical averaging, and f is assumed to have a certain amount of regularity in velocity. The result is that f is also regular in time and space, and this is related to a commutator identity introduced ...

Maximal Lp-Regularity for Stochastic Evolution Equations

We prove maximal L-regularity for the stochastic evolution equation

Maximal L-regularity for Stochastic Evolution Equations

We prove maximal Lp-regularity for the stochastic evolution equation{ dU(t) +AU(t) dt = F (t, U(t)) dt+B(t, U(t)) dWH(t), t ∈ [0, T ], U(0) = u0, under the assumption that A is a sectorial operator with a bounded H∞calculus of angle less than 1 2 π on a space Lq(O, μ). The driving process WH is a cylindrical Brownian motion in an abstract Hilbert space H. For p ∈ (2,∞) and q ∈ [2,∞) and initial...

Regularity of stochastic delay equations under pth order degeneracy

Regularity of Solutions to Stochastic Volterra Equations with Infinite Delay

The paper gives necessary and sufficient conditions providing regularity of solutions to stochastic Volterra equations with infinite delay on a ddimensional torus. The harmonic analysis techniques and stochastic integration in function spaces are used.